Kudelic R. Feedback Arc Set: A History of the Problem and Algorithms

Springer, 2022. — 134 p. — (SpringerBriefs in Computer Science).The feedback arc set problem is one of the quintessential problems of algorithmics and, more generally, of Computer Science. The main aim of the book is to give a review of all relevant information regarding a well-known and important problem of Feedback Arc Set (FAS). This review naturally also includes a history of the problem, as well as specific algorithms. To this point such work does not exist: There are sources where one can find incomplete and perhaps untrustworthy information. With this book, information about FAS can be found easily in one place: formulation, description, theoretical background, applications, algorithms, etc. Such a compendium will be of help to people involved in research, but also to people that want to quickly acquaint themselves with the problem and need reliable information. This research, professional work, and learning can proceed in a more streamlined and faster way.In this work, we will present a chronology of algorithms for a well-known classic Computer Science problem known under the name Feedback Arc Set (FAS).The problem can sometimes be found under the guise of a Quadratic Assignment (QA) problem since it can be formulated as such (with QA being a more general problem), and then solved by algorithms for the QA. At other times FAS can be found under the terminology of Linear Arrangement (LA), sequencing, or of Median Order. It is also possible to find it under the name Hitting Cycle (HC) problem since one has to hit every cycle in a collection of cycles. Sometimes it is possible to find it under a name of the Minimum Dominating Set problem.